Antenna array calibration for wireless charging

ABSTRACT

Antenna array calibration for wireless charging is disclosed. In one aspect, an initial calibration sequence is performed each time a wireless charging station is powered on. The initial calibration sequence utilizes a reference antenna element, which is an antenna element randomly selected from a plurality of antenna elements in the wireless charging station, to determine relative receiver phase errors between the reference antenna element and each of the other antenna elements in an antenna array. In another aspect, a training sequence is performed after completing the initial calibration sequence to determine total relative phase errors between the reference antenna element and each of the other antenna elements in the antenna array. Adjustments can then be made to match respective total relative phase errors among the plurality of antenna elements to achieve phase coherency among the plurality of antenna elements for improved wireless charging power efficiency.

PRIORITY APPLICATIONS

This application claims the benefit of U.S. provisional patentapplication Nos. 62/024,621, filed Jul. 15, 2014; 62/024,628, filed Jul.15, 2014; 62/051,023, filed Sep. 16, 2014; 62/052,517, filed Sep. 19,2014; 62/053,845, filed Sep. 23, 2014; and 62/052,822, filed Sep. 19,2014, which are incorporated herein by reference in their entireties.

FIELD OF THE DISCLOSURE

The technology of the disclosure relates generally to wireless chargingof a battery.

BACKGROUND

Mobile communication devices have become increasingly common in currentsociety. The prevalence of these mobile communication devices is drivenin part by the many functions that are now enabled on such devices.Demand for such functions increases processing capability requirementsfor the mobile communication devices. As a result, increasingly complexintegrated circuits (ICs) have been designed and manufactured to provideincreasingly greater functionality in the mobile communication devices.However, the increasingly complex ICs also tend to consume more batterypower during operation.

It has become more challenging to prolong battery life of the mobilecommunication devices in the face of continuing demand for higherprocessing speed, richer multimedia experience, and constantconnectivity. As a result, the mobile communication devices areincreasingly equipped with high-capacity batteries that are bothexpensive and space consuming. Even with the high-capacity batteries,the mobile communication devices often need to be plugged into the wallfor recharging before the day is over.

SUMMARY

Aspects disclosed in the detailed description include antenna arraycalibration for wireless charging. In this regard, a wireless chargingstation is provided and configured to calibrate a plurality of antennaelements in the wireless charging station. In one aspect, an initialcalibration sequence is performed each time the wireless chargingstation is powered on. The initial calibration sequence utilizes areference antenna element, which is an antenna element randomly selectedfrom the plurality of antenna elements, to determine relative receiverphase errors between the reference antenna element and each of the otherantenna elements in the antenna array. In another aspect, a trainingsequence is performed after completing the initial calibration sequence.The training sequence utilizes a wireless training signal and therelative receiver phase errors obtained in the initial calibrationsequence to determine total relative phase errors between the referenceantenna element and each of the other antenna elements in the antennaarray. Adjustments can then be made to match respective total relativephase errors among the plurality of antenna elements to achieve phasecoherency among the plurality of antenna elements for improved wirelesscharging power efficiency.

In this regard, in one aspect, a wireless charging station is provided.The wireless charging station comprises a plurality of antenna elements.Each of the plurality of antenna elements comprises a receiver and atransmitter coupled to an antenna. Each of the plurality of antennaelements also comprises a phase shift circuitry coupled to thetransmitter and configured to adjust transmitter phase of thetransmitter. The wireless charging station also comprises a controllercoupled to the plurality of antenna elements. The controller isconfigured to select a reference antenna element from the plurality ofantenna elements wherein unselected ones of the plurality of antennaelements are non-reference antenna elements. For each of thenon-reference antenna elements, the controller is configured to transmita first calibration signal from a transmitter of the reference antennaelement. For each of the non-reference antenna elements, the controlleris also configured to measure phase a_(x) of the first calibrationsignal at a receiver of the reference antenna element. For each of thenon-reference antenna elements, the controller is also configured tomeasure phase b_(x) of the first calibration signal at a receiver of anon-reference antenna element. For each of the non-reference antennaelements, the controller is also configured to transmit a secondcalibration signal from a transmitter of the non-reference antennaelement. For each of the non-reference antenna elements, the controlleris also configured to measure phase a_(y) of the second calibrationsignal at the receiver of the non-reference antenna element. For each ofthe non-reference antenna elements, the controller is also configured tomeasure phase b_(y) of the second calibration signal at the receiver ofthe reference antenna element (phase b_(y)). For each of thenon-reference antenna elements, the controller is also configured todetermine relative receiver phase error and relative transmitter phaseerror between the non-reference antenna element and the referenceantenna element based on the phase a_(x), the phase a_(y), the phaseb_(x), and the phase b_(y).

Those skilled in the art will appreciate the scope of the disclosure andrealize additional aspects thereof after reading the following detaileddescription in association with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings incorporated in and forming a part of thisspecification illustrate several aspects of the disclosure and, togetherwith the description, serve to explain the principles of the disclosure.

FIG. 1A is an exemplary illustration of a lithium-ion (Li-ion) batterycharging profile;

FIG. 1B is a capacity-voltage curve providing an exemplary illustrationof Li-ion battery capacity as a function of a charging voltage and acharging current;

FIG. 2 is a schematic diagram of an exemplary wireless charging system,in which a wireless charging station is configured to charge one or morewireless stations via one or more respective wireless radio frequency(RF) charging signals;

FIG. 3 is a schematic diagram of an exemplary wireless charging stationincluding a plurality of antenna elements that may be calibrated toachieve phase coherency when transmitting the one or more wireless RFcharging signals of FIG. 2;

FIG. 4 is a schematic diagram of an exemplary first configuration forperforming an initial calibration sequence among the plurality ofantenna elements of FIG. 3;

FIG. 5 is a schematic diagram of an exemplary second configuration forperforming an initial calibration sequence among the plurality ofantenna elements of FIG. 3;

FIG. 6 is a schematic diagram of an exemplary third configuration forperforming an initial calibration sequence among the plurality ofantenna elements of FIG. 3;

FIG. 7 is a schematic diagram of an exemplary configuration forperforming a training sequence among the plurality of antenna elementsof FIG. 3; and

FIG. 8 is a schematic diagram of an exemplary configuration forverifying phase coherency among the plurality of antenna elements ofFIG. 3.

DETAILED DESCRIPTION

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the disclosure andillustrate the best mode of practicing the disclosure. Upon reading thefollowing description in light of the accompanying drawings, thoseskilled in the art will understand the concepts of the disclosure andwill recognize applications of these concepts not particularly addressedherein. It should be understood that these concepts and applicationsfall within the scope of the disclosure and the accompanying claims.

Aspects disclosed in the detailed description include antenna arraycalibration for wireless charging. In this regard, a method forcalibrating a plurality of antenna elements of an antenna array in awireless charging station is provided. In one aspect, an initialcalibration sequence is performed each time the wireless chargingstation is powered on. The initial calibration sequence utilizes areference antenna element, which is an antenna element randomly selectedfrom the plurality of antenna elements, to determine relative receiverphase errors between the reference antenna element and each of the otherantenna elements in the antenna array. In another aspect, a trainingsequence is performed after completing the initial calibration sequence.The training sequence utilizes a wireless training signal and therelative receiver phase errors obtained in the initial calibrationsequence to determine total relative phase errors between the referenceantenna element and each of the other antenna elements in the antennaarray. Adjustments can then be made to match respective total relativephase errors among the plurality of antenna elements to achieve phasecoherency among the plurality of antenna elements for improved wirelesscharging power efficiency.

Before discussing the wireless charging concepts of the presentdisclosure, a brief overview of a lithium-ion (Li-ion) battery chargingprofile is provided with reference to FIGS. 1A and 1B. The discussion ofspecific exemplary aspects of wireless charging starts below withreference to FIG. 2.

In this regard, FIG. 1A is an exemplary illustration of a Li-ion batterycharging profile 10. As is well known in the industry, a Li-ion battery(not shown) has strict requirements on charging voltage and chargingcurrent because Li-ion cells (not shown) in the Li-ion battery cannotaccept overcharge. In this regard, the Li-ion battery can only take whatit can absorb. Anything extra can cause stress and even permanent damageto the Li-ion battery.

When the Li-ion battery is connected to a charging source (not shown) attime T₀, the Li-ion battery is in a constant current stage 12, in whichcharging voltage (referenced in drawings as V) rises while chargingcurrent (referenced in drawings as I) remains constant. As such, aneffective charging power (referenced in drawings as P_(EFF))(P_(EFF)=V×I) increases as a result of the charging voltage increase,thus enabling fast charging of the Li-ion battery. At time T₁, theLi-ion battery is in a saturation charge stage 14, in which the chargingvoltage peaks and levels off while the charging current starts todecline. As such, the effective charging power decreases as a result ofthe charging current decline. At time T₂, the Li-ion battery is in aready stage 16, wherein the Li-ion battery is charged to a desiredvoltage level and the charging current drops to zero (0). In thisregard, the effective charging power also drops to zero (0) to preventovercharging damage to the Li-ion battery. At time T₃, the Li-ionbattery is in a standby stage 18, in which the charging current may beapplied occasionally to top the Li-ion battery up to the desired voltagelevel.

FIG. 1B is a capacity-voltage curve 20 providing an exemplaryillustration of a Li-ion battery capacity as a function of the chargingvoltage and the charging current of FIG. 1A. The capacity-voltage curve20 comprises a capacity curve 22, a charging voltage curve 24, and acharging current curve 26. When the Li-ion battery is connected to thecharging source, the charging voltage curve 24 shoots up quickly. Inthis regard, the Li-ion battery is in the constant current stage 12according to the Li-ion battery charging profile 10 of FIG. 1A. As thecapacity curve 22 gradually peaks, the charging current curve 26declines quickly and the charging voltage curve 24 levels off. In thisregard, the Li-ion battery is in the saturation charge stage 14according to the Li-ion battery charging profile 10. Since the Li-ionbattery cannot accept overcharge, the charging current must be cut off.A continuous trickle charge (maintenance charge) would cause plating ofmetallic lithium, thus compromising safety of the Li-ion battery. Hence,according to the Li-ion battery charging profile 10 and thecapacity-voltage curve 20, the effective charging power increases whenthe Li-ion battery is in the constant current stage 12 and decreaseswhen the Li-ion battery is in the saturation charge stage 14 to ensurefast charging and protect the Li-ion battery from overcharging damage.

The Li-ion battery has become increasingly popular in battery-operatedelectronic devices, such as smartphones, tablets, and portablecomputers, due to many advantages over traditional batteries (e.g.,nickel-cadmium batteries). For example, the Li-ion battery has higherpower density, produces less self-discharge, and requires lowermaintenance to prolong battery life than the traditional batteries.Concurrent to the prevalence of Li-ion battery technology, wirelesscharging is also gaining traction in the wireless communication industryand may one day replace charging plugs and wires, similar to howBluetooth™ and wireless-fidelity (Wi-Fi) have eliminated communicationcables (e.g., Ethernet cables) in peer-to-peer and peer-to-multi-peercommunications.

In this regard, FIG. 2 is a schematic diagram of an exemplary wirelesscharging system 28, wherein a wireless charging station 30 is configuredto charge one or more wireless stations 32(1)-32(N) via one or morerespective wireless RF charging signals 34(1)-34(N). The one or morewireless stations 32(1)-32(N) include one or more respective batteries36(1)-36(N). In a non-limiting example, the one or more batteries36(1)-36(N) are Li-ion batteries. In this regard, the Li-ion batterycharging profile 10 of FIG. 1A and the capacity-voltage curve 20 of FIG.1B are applicable when charging the one or more batteries 36(1)-36(N) inthe wireless charging system 28. In another non-limiting example, theone or more wireless RF charging signals 34(1)-34(N) are provided on anindustrial, scientific, and medical (ISM) band that may operate in ninehundred fifteen megahertz (915 MHz), twenty-four hundred megahertz (2400MHz), fifty-eight hundred megahertz (5800 MHz), or twenty-four gigahertz(24 GHz) RF spectrums.

The wireless charging station 30 has a total available power (referencedin drawings as P_(TOTAL)), which must be set below a maximum power (notshown) that is set by regulatory authorities such as the FederalCommunications Commission (FCC) in the United States. The totalavailable power is shared among the one or more wireless stations32(1)-32(N). The wireless charging station 30 dynamically determines howthe total available power is distributed among the one or more wirelessstations 32(1)-32(N). In this regard, the more wireless stations thatare in the wireless charging system 28, the smaller share of the totalavailable power each wireless station will receive.

With continuing reference to FIG. 2, the wireless charging station 30includes a plurality of antenna elements (not shown). In a non-limitingexample, the wireless charging station 30 can have in excess of tenthousand (10,000) antenna elements. The plurality of antenna elements inthe wireless charging station 30 may be further configured to form oneor more antenna arrays 38(1)-38(N), in which each of the one or moreantenna arrays 38(1)-38(N) includes at least two antenna elements amongthe plurality of antenna elements of the wireless charging station 30.The one or more antenna arrays 38(1)-38(N) are configured to transmitthe one more wireless RF charging signals 34(1)-34(N) to the one or morewireless stations 32(1)-32(N), respectively. To illustrate theconfiguration and operation of the wireless charging system 28, wirelessstation 32(1), wireless RF charging signal 34(1), and antenna array38(1) are discussed as a non-limiting example. It should be understoodthat the configuration and operation discussed herein are applicable tothe one or more antenna arrays 38(1)-38(N), the one or more wireless RFcharging signals 34(1)-34(N), and the one or more wireless stations32(1)-32(N) as well.

If, for example, the antenna array 38(1) includes four antenna elements40(1)-40(4), the wireless RF charging signal 34(1) will include four RFsignals 42(1)-42(4) transmitted from the four antenna elements40(1)-40(4), respectively. In this regard, the wireless RF chargingsignal 34(1) is a beamformed wireless RF charging signal. Beamforming isa modern wireless signal transmission scheme, in which multiple wirelesssignals, such as the four RF signals 42(1)-42(4), are transmittedsimultaneously toward a single wireless receiver. If phases of themultiple wireless signals are coherent, the wireless receiver will beable to linearly combine the multiple wireless signals for improvedsignal strength and power gain.

Since the four RF signals 42(1)-42(4) may arrive at the wireless station32(1) through different paths, the four antenna elements 40(1)-40(4) inthe antenna array 38(1) are calibrated to ensure phase coherence whenthe four RF signals 42(1)-42(4) arrive at the wireless station 32(1). Byhaving the phase coherence among the four RF signals 42(1)-42(4), atotal RF power (referenced in drawings as P_(RF)) of the wireless RFcharging signal 34(1) can be linearly controlled by adjusting individualRF power of the four RF signals 42(1)-42(N). Hence, the total RF powerof the wireless RF charging signal 34(1) can be maximized.

If the antenna array 38(1) and the wireless station 32(1) are disposedin a line-of-sight (LOS) arrangement, transmitter phases and amplitudesof the four RF signals 42(1)-42(4) can be estimated based on a trainingsignal (not shown) provided by the wireless station 32(1) under theassumption that the training signal would have a high degree of phasecorrelation with the wireless RF charging signal 34(1). However, thismay not always be the case in the wireless charging system 28 becausethe antenna array 38(1) and the wireless station 32(1) may not always bedisposed in the LOS arrangement. When the antenna array 38(1) and thewireless station 32(1) are not disposed in the LOS arrangement, theestimated transmitter phases and amplitudes based on the training signalmay be inaccurate. As a result, it may be more difficult to preservephase coherence among the four RF signals 42(1)-42(4) and control thetotal RF power in the wireless RF charging signal 34(1). Consequently,it is also difficult for the wireless charging station 30 to control theeffective charging power according to the Li-ion battery chargingprofile 10 of FIG. 1A since the effective charging power isproportionally related to the total RF power. In this regard, one ormore battery charging signal indications (BCSIs) 44(1)-44(N) areprovided by one or more wireless charging circuits 46(1)-46(N) in theone or more wireless stations 32(1)-32(N), respectively, to help controlthe effective charging power according to the Li-ion battery chargingprofile 10.

For example, BCSI 44(1) provided by the wireless station 32(1) indicatesa difference between the effective charging power being provided tobattery 36(1) and a target charging power determined based on the Li-ionbattery charging profile 10 of FIG. 1A. In a non-limiting example, theBCSI 44(1) is set to zero (0) when the effective charging power isgreater than the target charging power to request a decrease of thetotal RF power in the wireless RF charging signal 34(1). In anothernon-limiting example, the BCSI 44(1) is set to one (1) when theeffective charging power is less than the target charging power torequest an increase of the total RF power in the wireless RF chargingsignal 34(1). Upon receiving the BCSI 44(1), the wireless chargingstation 30 adjusts the individual RF power of the four RF signals42(1)-42(4) accordingly. For example, the wireless charging station 30can decrease the individual RF power of the four RF signals 42(1)-42(4)if the BCSI 44(1) is set to zero (0), or increase the individual RFpower of the four RF signals 42(1)-42(4) when the BCSI 44(1) is set toone (1). Hence, by providing the BCSI 44(1) to the wireless chargingstation 30 continuously, or according to a predefined feedback schedule,the effective charging power provided to the battery 36(1) can begradually adjusted to eventually match the target charging power.

In addition to providing the one or more BCSIs 44(1)-44(N), the one ormore wireless stations 32(1)-32(N) may be configured to provide one ormore BCSI resolution (BCSIr) signals 44′(1)-44′(N). The one or moreBCSIr signals 44′(1)-44′(N) indicate one or more power differentialsbetween one or more effective charging powers provided to the one ormore batteries 36(1)-36(N) and one or more target charging powersrequired by the one or more batteries 36(1)-36(N), respectively.

As mentioned earlier, if phases of the multiple wireless signals, suchas the four RF signals 42(1)-42(4) transmitted by the antenna array38(1), are coherent, the wireless receiver at the wireless station 32(1)will be able to linearly combine the multiple wireless signals forimproved signal strength and power gain. To further illustrate how thewireless charging station 30 may be configured to transmit coherentlythe one more wireless RF charging signals 34(1)-34(N), FIG. 3 is aschematic diagram of an exemplary wireless charging station 48 includinga plurality of antenna elements 50(1)-50(M) that may be calibrated toachieve phase coherency when transmitting the one or more wireless RFcharging signals 34(1)-34(N) of FIG. 2.

With reference to FIG. 3, the plurality of antenna elements 50(1)-50(M)respectively include a plurality of receivers 52(1)-52(M) and aplurality of transmitters 54(1)-54(M). The plurality of receivers52(1)-52(M) and the plurality of transmitters 54(1)-54(M) arerespectively coupled to a plurality of antennas 56(1)-56(M) via aplurality of signal paths 58(1)-58(M). In a non-limiting example, theplurality of signal paths 58(1)-58(M) may be provided as coaxial cables.The plurality of transmitters 54(1)-54(M) may be powered by a powersource 60. The plurality of receivers 52(1)-52(M) is coupled to aplurality of receiver oscillators 62(1)-62(M) that determines operationfrequency of the plurality of receivers 52(1)-52(M), respectively. Theplurality of transmitters 54(1)-54(M) is coupled to a plurality oftransmitter oscillators 64(1)-64(M) that determines operation frequencyof the plurality of transmitters 54(1)-54(M), respectively.

The plurality of antenna elements 50(1)-50(M) comprises a plurality ofphase shift circuitries 66(1)-66(M), respectively. The plurality ofphase shift circuitries 66(1)-66(M) is coupled to the plurality oftransmitters 54(1)-54(M) and configured to adjust transmitter phases ofthe plurality of transmitters 54(1)-54(M), respectively. The pluralityof antenna elements 50(1)-50(M) also comprises a plurality of registers68(1)-68(M), respectively. The plurality of registers 68(1)-68(M) iscoupled to the plurality of phase shift circuitries 66(1)-66(M) andconfigured to store the transmitter phases of the plurality oftransmitters 54(1)-54(M), respectively, after being adjusted by theplurality of phase shift circuitries 66(1)-66(M).

The wireless charging station 48 comprises a controller 70 coupled tothe plurality of receivers 52(1)-52(M) and the plurality of transmitters54(1)-54(M). As is further discussed later with reference to FIGS. 4-9,the controller 70 is configured to collect a plurality of feedbackinformation 72(1)-72(M) from the plurality of receivers 52(1)-52(M),respectively. The controller 70 then controls the plurality of phaseshift circuitries 66(1)-66(M) to adjust the transmitter phases of theplurality of transmitters 54(1)-54(M) based on the plurality of feedbackinformation 72(1)-72(M), respectively.

The wireless charging station 48 also comprises a wireless communicationinterface 74, which may be configured to receive the one or more BCSIs44(1)-44(N) and the one or more BCSIr signals 44′(1)-44′(N) of FIG. 2.In a non-limiting example, the wireless communication interface 74 maybe configured to operate based on Wi-Fi, Bluetooth, Bluetooth Low Energy(BLE), and ZigBee communication protocols.

When the wireless charging station 48 is powered on, the transmitterphases of the plurality of antenna elements 50(1)-50(M) may be out ofalignment and become incoherent because relative phases of the pluralityof transmitter oscillators 64(1)-64(M) may be randomized at the power onevent. Furthermore, impedance variations among the plurality of signalpaths 58(1)-58(M) may also cause the plurality of antenna elements50(1)-50(M) to lose phase coherency during transmission. As such, it isnecessary to calibrate the plurality of antenna elements 50(1)-50(M) toensure phase coherency after power-up of the wireless charging station48.

Calibrations for the plurality of antenna elements 50(1)-50(M) may beconducted in several steps. In a first step (hereinafter referred to as“initial calibration sequence”), relative transmitter phase error andrelative receiver phase error is determined between each pair of antennaelements among the plurality of antenna elements 50(1)-50(M). Theinitial calibration sequence may be conducted with three differentconfigurations, which will be discussed with reference to FIGS. 4-6.After completing the initial calibration sequence, a second step(hereinafter referred to as “training sequence”) may be conducted tofurther determine total relative phase error between each pair ofantenna elements among the plurality of antenna elements 50(1)-50(M).The training sequence is illustrated and discussed with reference toFIG. 7. Subsequently, a third step (hereinafter referred to as“validation sequence”) may be performed to validate phase coherencyamong the plurality of antenna elements 50(1)-50(M). In a non-limitingexample, the validation sequence may be performed after the initialcalibration sequence and/or after the training sequence. The validationsequence is illustrated and discussed with reference to FIG. 8.

In this regard, FIG. 4 is a schematic diagram of an exemplary firstconfiguration 76 for performing the initial calibration sequence amongthe plurality of antenna elements 50(1)-50(M) of FIG. 3. Common elementsbetween FIGS. 3 and 4 are shown therein with common element numbers andwill not be re-described herein.

With reference to FIG. 4, to determine the relative transmitter phaseerror and the relative receiver phase error between each pair of antennaelements among the plurality of antenna elements 50(1)-50(M), thecontroller 70 designates an antenna element selected randomly from theplurality of antenna elements 50(1)-50(M) as a reference antennaelement. The controller 70 then determines the relative transmitterphase error and the relative receiver phase error between the referenceantenna element and each of the antenna elements among the plurality ofantenna elements 50(1)-50(M) not designated as the reference antennaelement (non-reference antenna element). For the convenience ofdiscussion, antenna element 50(X) and antenna element 50(Y), which maybe any of the plurality of antenna elements 50(1)-50(M), are discussedhereinafter in FIGS. 4-7 as the reference antenna element and thenon-reference antenna element, respectively. It should be understoodthat the configuration and operation discussed in connection to theantenna element 50(X) and the antenna element 50(Y) are applicable toall of the plurality of antenna elements 50(1)-50(M).

In a non-limiting example, the controller 70 may be configured toperform the initial calibration sequence according to the firstconfiguration 76. The controller 70 instructs the reference antennaelement 50(X) to transmit a first calibration signal 78 from respectivetransmitter 54(X) of the reference antenna element 50(X). The referenceantenna element 50(X) and the non-reference antenna element 50(Y)receive the first calibration signal 78 at respective receiver 52(X) andrespective receiver 52(Y). The controller 70 measures a respective phaseof the first calibration signal 78 at the receiver 52(X) (phase a_(x))and at the receiver 52(Y) (phase b_(x)). The phase a_(x) and the phaseb_(x) are both compounded by multiple factors that can be respectivelyexpressed by equations Eq. 1 and Eq. 2 below.phase a _(x) =T _(x) +λ+R _(X)  (Eq. 1)phase b _(x) =T _(X) +P _(XY) +R _(Y)  (Eq. 2)

With reference to the equations Eq. 1 and Eq. 2, T_(X) represents aphase shift associated with the transmitter 54(X) of the referenceantenna element 50(X). R_(X) represents a phase shift associated withthe receiver 52(X) of the reference antenna element 50(X). λ representsa phase shift associated with coupling the receiver 52(X) of thereference antenna element 50(X) to the transmitter 54(X) of thereference antenna element 50(X). R_(Y) represents a phase shiftassociated with the receiver 52(Y) of the non-reference antenna element50(Y). P_(XY) represents a phase shift associated with signal path 58(X)and signal path 58(Y) that convey the first calibration signal 78 fromthe transmitter 54(X) of the reference antenna element 50(X) to thereceiver 52(Y) of the non-reference antenna element 50(Y).

Subsequently, the controller 70 instructs the non-reference antennaelement 50(Y) to transmit a second calibration signal 80 from respectivetransmitter 54(Y) of the non-reference antenna element 50(Y). In anon-limiting example, the non-reference antenna element 50(Y) may beinstructed to transmit the second calibration signal 80 at a samefrequency as the first calibration signal 78 or at a different frequencyfrom the first calibration signal 78. The reference antenna element50(X) and the non-reference antenna element 50(Y) receive the secondcalibration signal 80 at the respective receiver 52(X) and therespective receiver 52(Y). The controller 70 then measures a respectivephase of the second calibration signal 80 at the receiver 52(X) (phaseb_(y)) and at the receiver 52(Y) (phase a_(y)). The phase a_(y) and thephase b_(y) are both compounded by multiple factors that can berespectively expressed by equations Eq. 3 and Eq. 4 below.phase a _(y) =T _(Y) +λ+R _(Y)  (Eq. 3)phase b _(y) =T _(Y) +P _(YX) +R _(X)  (Eq. 4)

With reference to the equations Eq. 3 and Eq. 4, T_(Y) represents aphase shift associated with the transmitter 54(Y) of the non-referenceantenna element 50(Y). R_(Y) represents a phase shift associated withthe receiver 52(Y) of the non-reference antenna element 50(Y). Δrepresents a phase shift associated with coupling the receiver 52(Y) ofthe non-reference antenna element 50(Y) to the transmitter 54(Y) of thenon-reference antenna element 50(Y). R_(X) represents a phase shiftassociated with the receiver 52(X) of the reference antenna element50(X). P_(YX) represents a phase shift associated with the signal path58(Y) and the signal path 58(X) that convey the second calibrationsignal 80 from the transmitter 54(Y) of the non-reference antennaelement 50(Y) to the receiver 52(X) of the reference antenna element50(X).

As previously mentioned, the purpose of the initial calibration sequenceis to determine the relative transmitter phase error and the relativereceiver phase error among the plurality of antenna elements50(1)-50(M). In this regard, the relative transmitter phase error andthe relative receiver phase error between the non-reference antennaelement 50(Y) and the reference antenna element 50(X) can be determinedby equations Eq. 5 and Eq. 6 below.relative transmitter phase error=T _(Y) −T _(X)  (Eq. 5)relative receiver phase error=R _(Y) −R _(X)  (Eq. 6)

Assuming that P_(XY) and P_(YX) are equal, the equations Eq. 5 and Eq. 6can be transformed to the following equations Eq. 7 and Eq. 8,respectively, based on the equations Eq. 1, Eq. 2, Eq. 3, and Eq. 4.T _(Y) −T _(X)=[(a _(y) −a _(x))+(b _(y) −b _(x))]/2  (Eq. 7)R _(Y) −R _(X)=[(a _(y) −a _(x))−(b _(y) −b _(x))]/2  (Eq. 8)

Hence, the relative transmitter phase error (T_(Y)−T_(x)) and therelative receiver phase error (R_(Y)−R_(X)) can be determined based onthe phase a_(x), the phase a_(y), the phase b_(x), and the phase b_(y)that are measured by the controller 70 during the initial calibrationsequence.

FIG. 5 is a schematic diagram of an exemplary second configuration 82for performing the initial calibration sequence among the plurality ofantenna elements 50(1)-50(M) of FIG. 3. Common elements between FIGS. 3,4, and 5 are shown therein with common element numbers and will not bere-described herein.

To perform the initial calibration sequence based on the secondconfiguration 82, a calibration antenna element 84, which is identicalto the plurality of antenna elements 50(1)-50(M), is provided in thewireless charging station 48. The controller 70 instructs the referenceantenna element 50(X) to transmit a first calibration signal 86 from thetransmitter 54(X) of the reference antenna element 50(X). The referenceantenna element 50(X) and the calibration antenna element 84 receive thefirst calibration signal 86 at the respective receiver 52(X) and acalibration receiver 88. The controller 70 then measures a respectivephase of the first calibration signal 86 at the respective receiver52(X) (phase a_(x)) and at the calibration receiver 88 (phase b_(y)).The phase a_(x) and the phase b_(x) are both compounded by multiplefactors that can be respectively expressed by equations Eq. 9 and Eq. 10below.phase a _(x) =T _(X) +λ+R _(X)  (Eq. 9)phase b _(x) =T _(X) +P _(X)  (Eq. 10)

With reference to the equations Eq. 9 and Eq. 10, T_(X) represents aphase shift associated with the transmitter 54(X) of the referenceantenna element 50(X). R_(X) represents a phase shift associated withthe receiver 52(X) of the reference antenna element 50(X). λ representsa phase shift associated with coupling respective receiver 52(X) of thereference antenna element 50(X) to the transmitter 54(X) of thereference antenna element 50(X). P_(X) represents a phase shiftassociated with the signal path 58(X) and a signal path 90 in thecalibration antenna element 84 that convey the first calibration signal86 from the transmitter 54(X) of the reference antenna element 50(X) tothe calibration receiver 88 of the calibration antenna element 84.

Next, the controller 70 instructs the non-reference antenna element50(Y) to transmit a second calibration signal 92 from the respectivetransmitter 54(Y) of the non-reference antenna element 50(Y). Thenon-reference antenna element 50(Y) and the calibration antenna element84 receive the second calibration signal 92 at the respective receiver52(Y) and the calibration receiver 88. The controller 70 then measures arespective phase of the second calibration signal 92 at the respectivereceiver 52(Y) (phase a_(y)) and at the calibration receiver 88 (phaseb_(y)). The phase a_(y) and the phase b_(y) are both compounded bymultiple factors that can be respectively expressed by equations Eq. 11and Eq. 12 below.phase a _(y) =T _(Y) +λ+R _(Y)  (Eq. 11)phase b _(y) =T _(Y) +P _(Y)  (Eq. 12)

With reference to the equations Eq. 11 and Eq. 12, T_(Y) represents aphase shift associated with the transmitter 54(Y) of the non-referenceantenna element 50(Y). R_(Y) represents a phase shift associated withthe receiver 52(Y) of the non-reference antenna element 50(Y). λrepresents a phase shift associated with coupling the receiver 52(Y) ofthe non-reference antenna element 50(Y) to the transmitter 54(Y) of thenon-reference antenna element 50(Y). P_(Y) represents a phase shiftassociated with the signal path 58(Y) and the signal path 90 in thecalibration antenna element 84 that convey the second calibration signal92 from the transmitter 54(Y) of the non-reference antenna element 50(Y)to the calibration receiver 88 of the calibration antenna element 84.

Subsequently, the controller 70 instructs the calibration antennaelement 84 to transmit a third calibration signal 94 from a calibrationtransmitter 96 of the calibration antenna element 84. The receiver 52(X)of the reference antenna element 50(X) and the receiver 52(Y) of thenon-reference antenna element 50(Y) receive the third calibration signal94. The controller 70 then measures a respective phase of the thirdcalibration signal 94 at the receiver 52(X) (phase c_(x)) and at thereceiver 52(Y) (phase c_(y)). The phase c_(x) and the phase c_(y) arecompounded by multiple factors that can be respectively expressed byequations Eq. 13 and Eq. 14 below.phase c _(x) =R _(X) +Δ+P _(X)  (Eq. 13)phase c _(y) =R _(Y) +Δ+P _(Y)  (Eq. 14)

With reference to the equations Eq. 13 and Eq. 14, Δ represents a phasedifferential between the calibration transmitter 96 and the calibrationreceiver 88 of the calibration antenna element 84.

Accordingly, the relative receiver phase error (R_(Y)−R_(X)) between thenon-reference antenna element 50(Y) and the reference antenna element50(X) can be determined based on the equations Eq. 9-14 and expressed bythe equation (Eq. 15) below.R _(Y) −R _(X)=[(c _(y) −b _(y) +a _(y))−(c _(x) −b _(x) +a_(x))]/2  (Eq. 15)

Hence, the relative receiver phase error (R_(Y)−R_(X)) can be determinedbased on the phase a_(x), the phase a_(y), the phase b_(x), the phaseb_(y), the phase c_(x), and the phase c_(y) that are measured by thecontroller 70 during the initial calibration sequence.

FIG. 6 is a schematic diagram of an exemplary third configuration 98 forperforming the initial calibration sequence among the plurality ofantenna elements 50(1)-50(M) of FIG. 3. Common elements between FIGS. 3,4, 5, and 6 are shown therein with common element numbers and will notbe re-described herein.

To perform the initial calibration sequence based on the thirdconfiguration 98, a calibration device 100 is provided outside thewireless charging station 48. The controller 70 instructs the referenceantenna element 50(X) to transmit a first calibration signal 102 fromthe transmitter 54(X) of the reference antenna element 50(X). Thereceiver 52(X) of the reference antenna element 50(X) and a receiver(not shown) of the calibration device 100 receive the first calibrationsignal 102. The controller 70 then measures a respective phase of thefirst calibration signal 102 at the receiver 52(X) (phase a_(x)) and atthe receiver of the calibration device 100 (phase b_(x)). The phasea_(x) and the phase b_(x) are both compounded by multiple factors thatcan be respectively expressed by equations Eq. 16 and Eq. 17 below.phase a _(x) =T _(X) +λ+R _(X)  (Eq. 16)phase b _(x) =T _(X) +P _(X)  (Eq. 17)

With reference to the equations Eq. 16 and Eq. 17, P_(X) represents amultipath phase shift associated with the signal path 58(X) and awireless path 104 to the calibration device 100 that convey the firstcalibration signal 102 from the transmitter 54(X) of the referenceantenna element 50(X) to the receiver of the calibration device 100.

Next, the controller 70 instructs the non-reference antenna element50(Y) to transmit a second calibration signal 106 from the transmitter54(Y) of the non-reference antenna element 50(Y). The receiver 52(Y) ofthe non-reference antenna element 50(Y) and the receiver of thecalibration device 100 receive the second calibration signal 106. Thecontroller 70 then measures a respective phase of the second calibrationsignal 106 at the receiver 52(Y) (phase a_(y)) and at the receiver ofthe calibration device 100 (phase b_(y)). The phase a_(y) and the phaseb_(y) are both compounded by multiple factors that can be respectivelyexpressed by equations Eq. 18 and Eq. 19 below.phase a _(y) =T _(Y) +λ+R _(Y)  (Eq. 18)phase b _(y) =T _(Y) +P _(Y)  (Eq. 19)

With reference to the equations Eq. 18 and Eq. 19, P_(Y) represents amultipath phase shift associated with the signal path 58(Y) and awireless path 108 to the calibration device 100 that convey the secondcalibration signal 106 from the transmitter 54(Y) of the non-referenceantenna element 50(Y) to the receiver of the calibration device 100.

Subsequently, a third calibration signal 110 is transmitted from atransmitter (not shown) of the calibration device 100. The receiver52(X) of the reference antenna element 50(X) and the receiver 52(Y) ofthe non-reference antenna element 50(Y) receive the third calibrationsignal 110. The controller 70 measures a respective phase of the thirdcalibration signal 110 at the receiver 52(X) (phase c_(x)) and at thereceiver 52(Y) (phase c_(y)). The phase c_(x) and the phase c_(y) arecompounded by multiple factors that can be expressed by equations Eq. 20and Eq. 21 below.phase c _(x) =R _(X) +Δ+P _(X)  (Eq. 20)phase c _(y) =R _(Y) +Δ+P _(Y)  (Eq. 21)

With reference to the equations Eq. 20 and Eq. 21, Δ represents a phasedifferential between the transmitter and the receiver of the calibrationdevice 100.

The calibration device 100 may communicate the phase b_(x) and the phaseb_(y) to the controller 70 via a wireless link 112. In a non-limitingexample, the wireless link 112 operates in one of the ISM bands. Inanother non-limiting example, the wireless link 112 may operate based onWi-Fi, Bluetooth, BLE, and ZigBee communication protocols. In anothernon-limiting example, the wireless link 112 may be established betweenthe calibration device 100 and the wireless communication interface 74in the wireless charging station 48.

Accordingly, the relative receiver phase error (R_(Y)−R_(X)) between thenon-reference antenna element 50(Y) and the reference antenna element50(X) can be determined based on the equations Eq. 16-21 and expressedby equation Eq. 22 below.R _(Y) −R _(X)=[(c _(y) −b _(y) +a _(y))−(c _(x) −b _(x) +a_(x))]/2  (Eq. 22)

Hence, the relative receiver phase error (R_(Y)−R_(X)) can be determinedbased on the phase a_(x), the phase a_(y), the phase b_(x), the phaseb_(y), the phase c_(x), and the phase c_(y), which can be measured andrecorded by the controller 70 during the initial calibration sequence.

As previously mentioned, after completing the initial calibrationsequence, the training sequence may be conducted to further determinethe total relative phase error between each pair of antenna elementsamong the plurality of antenna elements 50(1)-50(M). In this regard,FIG. 7 is a schematic diagram of an exemplary configuration 114 forperforming the training sequence among the plurality of antenna elements50(1)-50(M) of FIG. 3. Common elements between FIGS. 3, 4, 5, 6, and 7are shown therein with common element numbers and will not bere-described herein.

To perform the training sequence, a training device 116 transmits awireless training signal 118 to the plurality of antenna elements50(1)-50(M) in the wireless charging station 48. The receiver 52(X) ofthe reference antenna element 50(X) and the receiver 52(Y) of thenon-reference antenna element 50(Y) receive the wireless training signal118 simultaneously. The controller 70 measures a respective phase of thewireless training signal 118 at the receiver 52(X) (phase t_(x)) and atthe receiver 52(Y) (phase t_(y)). The phase t_(x) and the phase t_(y)are both compounded by multiple factors that can be expressedrespectively by equations Eq. 23 and Eq. 24 below.phase t _(x) =R _(X) +P _(X)+Δ  (Eq. 23)phase t _(y) =R _(Y) +P _(Y)+Δ  (Eq. 24)

With reference to the equations Eq. 23 and Eq. 24, P_(X) represents amultipath phase shift experienced by the wireless training signal 118when traveling from a transmitter of the training device 116 to thereceiver 52(X) of the reference antenna element 50(X). P_(Y) representsa multipath phase shift experienced by the wireless training signal 118when traveling from the transmitter (not shown) of the training device116 to the receiver 52(Y) of the non-reference antenna element 50(Y). Δrepresents a phase differential between the transmitter and a receiver(not shown) in the training device 116.

Using the phase t_(x) and the phase t_(y) in connection with the phasea_(x) and the phase a_(y), which have been respectively determinedduring the initial calibration sequence according to the equations Eq.1, 9, and 16 and the equations Eq. 2, 10, and 17, it is possible for thecontroller 70 to estimate a respective transmitter phase of thereference antenna element (φ_(X)) and a respective transmitter phase ofthe non-reference antenna element (φ_(Y)) based on the followingequations Eq. 25 and Eq. 26, respectively.φ_(X) =T _(X) +P _(X) =a _(x) +t _(x)−2R _(X)−λ−Δ  (Eq. 25)φ_(Y) =T _(Y) +P _(Y) =a _(y) +t _(y)−2R _(Y)−λ−Δ  (Eq. 26)

Based on the equations Eq. 25 and Eq. 26, the controller 70 candetermine a total relative phase error (φ_(Y)−φ_(X)) between thenon-reference antenna element 50(Y) and the reference antenna element50(X) based on equation Eq. 27 below.φ_(Y)−φ_(X)=(a _(y) +t _(y))−(a _(x) +t _(x))−2(R _(Y) −R _(X))  (Eq.27)

With reference to the equation Eq. 27, R_(Y)−R_(X) represents therelative receiver phase error between the non-reference antenna element50(Y) and the reference antenna element 50(X), which has been determinedduring the initial calibration sequence. In this regard, if the initialcalibration sequence is conducted based on the first configuration 76 ofFIG. 4, the controller 70 can determine the relative receiver phaseerror (R_(Y)−R_(X)) based on the equation Eq. 8. Thus, by substitutingthe R_(Y)−R_(X) in the equation Eq. 27 with the R_(Y)−R_(X) in theequation Eq. 8, the total relative phase error (φ_(Y)−φ_(X)) can beexpressed as equation Eq. 28 below.φ_(Y)−φ_(X)=(b _(y) +t _(y))−(b _(x) +t _(x))  (Eq. 28)

If the initial calibration sequence is conducted based on the secondconfiguration 82 of FIG. 5 or the third configuration 98 of FIG. 6, therelative receiver phase error (R_(Y)−R_(X)) is determined by either theequation Eq. 15 or the equation Eq. 22. Thus, by substituting theR_(Y)−R_(X) in the equation Eq. 27 with the R_(Y)−R_(X) in the equationEq. 15 or the equation Eq. 22, the total relative phase error(φ_(Y)−φ_(X)) can be expressed as equation Eq. 29 below.φ_(Y)−φ_(X)=(t _(y) +b _(y) −c _(y))−(t _(x) +b _(x) −c _(x))  (Eq. 29)

The training sequence described above is based on an assumption thatsome kind of reciprocity exists between the training device 116 and theplurality of antenna elements 50(1)-50(M). That is, the multipathamplitude and phase changes experienced by the wireless training signal118 are the same as the amplitude and phase changes the plurality ofantenna elements 50(1)-50(M) would experience when transmitting wirelessRF charging signals. Because of this reciprocity assumption, it ispossible for the controller 70 to estimate the total relative phaseerror (φ_(Y)−φ_(X)) between the non-reference antenna element 50(Y) andthe reference antenna element 50(X) based on the multipath phase shiftsP_(X) and P_(Y) of the wireless training signal 118 in the equations Eq.25-27. However, the reciprocity assumption may not always be true.Hence, it may be necessary to validate phase coherence among theplurality of antenna elements 50(1)-50(X) after conducting the initialcalibration sequence and the training sequence.

In this regard, FIG. 8 is a schematic diagram of an exemplaryconfiguration 120 for verifying phase coherency among the plurality ofantenna elements 50(1)-50(M). Common elements between FIGS. 3, 4, and 8are shown therein with common element numbers and will not bere-described herein.

With reference to FIG. 8, the controller 70 instructs the plurality ofantenna elements 50(1)-50(M) to transmit a plurality of wireless signals122(1)-122(M) to a receiving device 124. The receiving device 124provides a first power measurement 126, which indicates a first totalpower received from the plurality of wireless signals 122(1)-122(M), tothe controller 70 via a wireless link 128. In a non-limiting example,the wireless link 128 operates in one of the ISM bands. In anothernon-limiting example, the wireless link 128 may operate based on Wi-Fi,Bluetooth, BLE, and ZigBee communication protocols. In anothernon-limiting example, the wireless link 128 may be established betweenthe receiving device 124 and the wireless communication interface 74 inthe wireless charging station 48.

The controller 70 then instructs at least one antenna element among theplurality of antenna elements 50(1)-50(M) to increase power level of atleast one wireless signal among the plurality of wireless signals122(1)-122(M) by a predetermined amount P_(UP). The receiving device 124subsequently provides a second power measurement 130, which indicates asecond total power received from the plurality of wireless signals122(1)-122(M), to the controller 70 via the wireless link 128. If phasecoherency exists among the plurality of antenna elements 50(1)-50(M),the second power measurement 130 shall increase from the first powermeasurement 126 by the predetermined amount P_(UP). If the second powermeasurement 130 does not increase from the first power measurement 126by the predetermined amount P_(UP), it can be concluded that theplurality of antenna elements 50(1)-50(M) are phase incoherent.

Those skilled in the art will recognize improvements and modificationsto the embodiments of the present disclosure. All such improvements andmodifications are considered within the scope of the concepts disclosedherein and the claims that follow.

What is claimed is:
 1. A wireless charging station, comprising: aplurality of antenna elements each comprising: a receiver and atransmitter coupled to an antenna; and a phase shift circuitry coupledto the transmitter and configured to adjust transmitter phase of thetransmitter; and a controller coupled to the plurality of antennaelements and configured to: select a reference antenna element from theplurality of antenna elements wherein unselected ones of the pluralityof antenna elements are non-reference antenna elements; and for each ofthe non-reference antenna elements: transmit a first calibration signalfrom a transmitter of the reference antenna element; measure phase a_(x)of the first calibration signal at a receiver of the reference antennaelement; measure phase b_(x) of the first calibration signal at areceiver of a non-reference antenna element; transmit a secondcalibration signal from a transmitter of the non-reference antennaelement; measure phase a_(y) of the second calibration signal at thereceiver of the non-reference antenna element; measure phase b_(y) ofthe second calibration signal at the receiver of the reference antennaelement; and determine relative receiver phase error and relativetransmitter phase error between the non-reference antenna element andthe reference antenna element based on the phase a_(x), the phase a_(y),the phase b_(x), and the phase b_(y).
 2. The wireless charging stationof claim 1 wherein: each of the plurality of antenna elements furthercomprises a register; and the controller is further configured to storethe relative receiver phase error and the relative transmitter phaseerror in the register of the reference antenna element and the registerof the non-reference antenna element.
 3. The wireless charging stationof claim 1 wherein the controller is further configured to: instruct theplurality of antenna elements to transmit a plurality of wirelesssignals to a receiving device, respectively; receive a first powermeasurement from the receiving device indicating a first total powerreceived by the receiving device from the plurality of wireless signals;instruct at least one of the plurality of antenna elements to increasepower level of at least one respective wireless signal by apredetermined amount; receive a second power measurement from thereceiving device indicating a second total power received by thereceiving device from the plurality of wireless signals; determine thatthe plurality of antenna elements is phase coherent if the second powermeasurement increases from the first power measurement by thepredetermined amount; and determine that the plurality of antennaelements is phase incoherent if the second power measurement does notincrease from the first power measurement by the predetermined amount.4. The wireless charging station of claim 3 wherein the controller isfurther configured to receive the first power measurement and the secondpower measurement via a wireless link in one of the industrial,scientific, and medical (ISM) bands.
 5. The wireless charging station ofclaim 1 wherein the controller is further configured to: configure theplurality of antenna elements to receive a wireless training signal froma training device; measure phase t_(x) of the wireless training signalat the receiver of the reference antenna element; estimate transmitterphase of the reference antenna element based on the phase t_(x); and foreach of the non-reference antenna elements: measure phase t_(y) of thewireless training signal at the receiver of the non-reference antennaelement; estimate transmitter phase of the non-reference antenna elementbased on the phase t_(y); and determine total relative phase errorbetween the transmitter phase of the non-reference antenna element andthe transmitter phase of the reference antenna element.
 6. The wirelesscharging station of claim 5 wherein the controller is further configuredto match the total relative phase error among the plurality of antennaelements.
 7. The wireless charging station of claim 5 wherein thecontroller is further configured to: instruct the plurality of antennaelements to transmit a plurality of wireless signals to a receivingdevice, respectively; receive a first power measurement from thereceiving device indicating a first total power received by thereceiving device from the plurality of wireless signals; instruct atleast one of the plurality of antenna elements to increase power levelof at least one wireless signal by a predetermined amount; receive asecond power measurement from the receiving device indicating a secondtotal power received by the receiving device from the plurality ofwireless signals; determine that the plurality of antenna elements isphase coherent if the second power measurement increases from the firstpower measurement by the predetermined amount; and determine that theplurality of antenna elements is phase incoherent if the second powermeasurement does not increase from the first power measurement by thepredetermined amount.
 8. The wireless charging station of claim 7wherein the controller is further configured to receive the first powermeasurement and the second power measurement via a wireless link in oneof the industrial, scientific, and medical (ISM) bands.
 9. The wirelesscharging station of claim 5 wherein the controller is further configuredto determine the total relative phase error between the transmitterphase of the non-reference antenna element and the transmitter phase ofthe reference antenna element by adding the phase t_(y) and the phaseb_(y) and subtracting the phase t_(x) and the phase b_(x).
 10. Thewireless charging station of claim 5 wherein the controller is furtherconfigured to measure the phase t_(x) by calculating a sum of: a phaseshift (R_(X)) associated with the receiver of the reference antennaelement; a multipath phase shift (P_(X)) experienced by the wirelesstraining signal when traveling from a transmitter of the training deviceto the receiver of the reference antenna element; and a phasedifferential (Δ) between the transmitter and a receiver in the trainingdevice.
 11. The wireless charging station of claim 5 wherein thecontroller is further configured to measure the phase t_(y) bycalculating a sum of: a phase shift (R_(Y)) associated with the receiverof the non-reference antenna element; a multipath phase shift (P_(Y))experienced by the wireless training signal when traveling from atransmitter of the training device to the receiver of the non-referenceantenna element; and a phase differential (Δ) between the transmitterand a receiver in the training device.
 12. The wireless charging stationof claim 5 wherein the plurality of antenna elements is configured toreceive the wireless training signal at a same frequency as the firstcalibration signal and the second calibration signal.
 13. The wirelesscharging station of claim 1 wherein the controller is further configuredto determine the relative receiver phase error between the non-referenceantenna element and the reference antenna element by: calculating afirst sum by adding the phase a_(y) and the phase b_(x); calculating asecond sum by adding the phase a_(x) and the phase b_(y); andsubtracting the second sum from the first sum and then dividing by two.14. The wireless charging station of claim 1 wherein the controller isfurther configured to determine the relative transmitter phase errorbetween the non-reference antenna element and the reference antennaelement by: calculating a first sum by adding the phase a_(y) and thephase b_(y); calculating a second sum by adding the phase a_(x) and thephase b_(x); and subtracting the second sum from the first sum and thendividing by two.
 15. The wireless charging station of claim 1 whereinthe controller is further configured to measure the phase a_(x) bycalculating a sum of: a phase shift (T_(X)) associated with thetransmitter of the reference antenna element; a phase shift (R_(X))associated with the receiver of the reference antenna element; and aphase shift (λ) associated with coupling the receiver of the referenceantenna element to the transmitter of the reference antenna element toreceive the first calibration signal.
 16. The wireless charging stationof claim 1 wherein the controller is further configured to measure thephase a_(y) by calculating a sum of: a phase shift (T_(Y)) associatedwith the transmitter of the non-reference antenna element; a phase shift(R_(Y)) associated with the receiver of the non-reference antennaelement; and a phase shift (λ) associated with coupling the receiver ofthe non-reference antenna element to the transmitter of thenon-reference antenna element to receive the second calibration signal.17. The wireless charging station of claim 1 wherein the controller isfurther configured to measure the phase b_(x) by calculating a sum of: aphase shift (T_(X)) associated with the transmitter of the referenceantenna element; a phase shift (R_(Y)) associated with the receiver ofthe non-reference antenna element; and a phase shift (P_(XY)) associatedwith a signal path that conveys the first calibration signal from thetransmitter of the reference antenna element to the receiver of thenon-reference antenna element.
 18. The wireless charging station ofclaim 1 wherein the controller is further configured to measure thephase b_(y) by calculating a sum of: a phase shift (T_(Y)) associatedwith the transmitter of the non-reference antenna element; a phase shift(R_(X)) associated with the receiver of the reference antenna element;and a phase shift (P_(YX)) associated with a signal path that conveysthe second calibration signal from the receiver of the non-referenceantenna element to the transmitter of the reference antenna element. 19.The wireless charging station of claim 1 wherein the non-referenceantenna element is configured to transmit the second calibration signalat a same frequency as the first calibration signal.
 20. The wirelesscharging station of claim 1 wherein the non-reference antenna element isconfigured to transmit the second calibration signal at a differentfrequency from the first calibration signal.